The Floodlight Problem
Abstract
Given three angles summing to 2π, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specified angles not exceeding π can be placed at n fixed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2π. We give O(nlog n) algorithms for both these problems.
Part of this work was carried out when the authors were participants of the 1992 Workshop on Graph Theory and Computational Geometry at the Bellairs Research Institute of McGill University. A preliminary version appeared in the Proceedings of the 5th Canadian Conference on Computational Geometry, 1993.
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